All Questions ⁺⁰236075 Questions

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Algebra

Ruth has a beaker containing a solution of $800$ mL of acid and $200$ mL of water. She thinks the solution is a little strong, so she drains $700$ mL from the beaker, adds $700$ mL of water, and stirs the solution. Ruth thinks the solution is read more ..

MEMEG0D Nov 23, 2024

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5

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+781

Algebra

Compute
1 + \frac{3}{6} + \frac{5}{6^2} + \frac{7}{6^3} + 2 + \frac{2}{5} + \frac{2}{5^3} + \frac{2}{5^4}

booboo44 Nov 23, 2024

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3

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+781

Algebra

Find all values of c such that 3(2c + 1) = 28*(3c) - 9 + 45(3c) - 18. If you find more than one value of c, then list your values in increasing order, separated by commas.

booboo44 Nov 23, 2024

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+781

Algebra

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
2ab - 12a + 3a + 3b - 8b - ab + ___

booboo44 Nov 23, 2024

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+781

Algebra

Simplify \frac{4}{1 - \sqrt[3]{3}} + \sqrt[3]{9}.

booboo44 Nov 23, 2024

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2

+781

Algebra

Sophie's favorite number is a two-digit number. If she reverses the digits, the result is $45$ less than her favorite number. The sum of the digits in her favorite number is $6$. What is Sophie's favorite number?

booboo44 Nov 23, 2024

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6

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+781

Algebra

Anna has a collection of $120$ marbles, each of which is either red or blue. If Anna has $135$ more red marbles than blue marbles, how many blue marbles does she have?

booboo44 Nov 23, 2024

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+781

Algebra

Find all real numbers $a$ that satisfy
\frac{1}{a^3 + 7} -7 = -\frac{a}{a^3 + 7}.

booboo44 Nov 23, 2024

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2

+781

Algebra

What is the smallest positive integer n such that \sqrt[4]{675 + n} is an integer?

booboo44 Nov 23, 2024

Nov 22, 2024

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+781

Geometry

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

booboo44 Nov 22, 2024

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8

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+781

Geometry

Points $A$, $B$, and $C$ are on a circle such that $AB = 8$, $BC = 15$, and $AC = 12$. Find the radius of the circle.

booboo44 Nov 22, 2024

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+781

Geometry

In triangle $ABC$, $M$ is the midpoint of $\overline{BC}$, and $N$ is the midpoint of $\overline{AC}$. The perpendicular bisectors of $BC$ and $AC$ intersect at a point $O$ inside the triangle. If $\angle AOB = 90^\circ$, then find the measure read more ..

booboo44 Nov 22, 2024

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+781

Geometry

Let G be the center of equilateral triangle XYZ A dilation centered at G with scale factor -1 is applied to triangle XYZ to obtain triangle X'Y'Z' Let A be the area of the region that is contained inside both triangles XYZ and X'Y'Z' Find read more ..

booboo44 Nov 22, 2024

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+310

Counting

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

MEMEG0D Nov 22, 2024

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+310

Counting

In how many ways can you distribute $8$ indistinguishable balls among $2$ distinguishable boxes, if at least one of the boxes must be empty?

MEMEG0D Nov 22, 2024

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+310

Counting

There is a group of five children, where two of the children are twins. In how many ways can I distribute $8$ identical pieces of candy to the children, if the twins must get at least one piece of candy each?

MEMEG0D Nov 22, 2024

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+809

Algebra

For an integer n, the inequality
x^2 + nx + 15 < -21 - 7x + x^2
has no real solutions in x. Find the number of different possible values of n.

gnistory Nov 22, 2024

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5

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+1520

Number Theory

Find the smallest positive integer B so that when we express the decimal number 250 as a base B number, we still get a 2-digit number.

blackpanther Nov 22, 2024

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+1520

Number Theory

Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$

blackpanther Nov 22, 2024

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+1520

Number Theory

What are the first 5 digits after the decimal point (technically the hexadecimal point...) when the fraction \frac{2}{23} is written in base 16?
Express your answer as a five digit hexadecimal number. You do not need to include read more ..

blackpanther Nov 22, 2024

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+1520

Number Theory

Let N be a positive integer. The number N has three digits when expressed in base 7. When the number N is expressed in base 5, it has the same three digits, in reverse order. What is N? (Express your answer in decimal.)

blackpanther Nov 22, 2024

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+441

Algebra

Let $x$ and $y$ be real numbers such that $x^2 + y^2 = 4x + 12y.$ Find the largest possible value of $x + y.$ Give your answer in exact form using radicals, simplified as far as possible.

crimefightingvigiI Nov 22, 2024

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